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Simplifying 2x(x + 2) = 1 + 5x Reorder the terms: 2x(2 + x) = 1 + 5x (2 * 2x + x * 2x) = 1 + 5x (4x + 2x2) = 1 + 5x Solving 4x + 2x2 = 1 + 5x Solving for variable 'x'. Reorder the terms: -1 + 4x + -5x + 2x2 = 1 + 5x + -1 + -5x Combine like terms: 4x + -5x = -1x -1 + -1x + 2x2 = 1 + 5x + -1 + -5x Reorder the terms: -1 + -1x + 2x2 = 1 + -1 + 5x + -5x Combine like terms: 1 + -1 = 0 -1 + -1x + 2x2 = 0 + 5x + -5x -1 + -1x + 2x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -1 + -1x + 2x2 = 0 Factor a trinomial. (-1 + -2x)(1 + -1x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-0.5, 1}
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